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The equivalent resistance between points A and B of the resistors shown in the figure is 35 Ω

To solve for the unknown resistance \( R \) in this circuit, we need to analyze the configuration of resistors.

### Step 1: Identify the circuit configuration
- The 12 Ω resistor is in series with the combination of the 55 Ω and \( R \) resistors, which are in parallel.

### Step 2: Determine the total resistance
You mentioned that the total resistance between points A and B is given as 35 Ω. We can use this information to set up an equation.

#### Parallel combination of 55 Ω and \( R \):
The formula for the equivalent resistance \( R_{\text{eq}} \) of two resistors in parallel is:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R} + \frac{1}{55}
\]
Solving for \( R_{\text{eq}} \):
\[
R_{\text{eq}} = \frac{55R}{55 + R}
\]

#### Total resistance from A to B:
The total resistance \( R_{\text{total}} \) is the sum of the 12 Ω resistor and the parallel combination:
\[
R_{\text{total}} = 12 + R_{\text{eq}} = 35 \, \Omega
\]
Substitute the expression for \( R_{\text{eq}} \):
\[
12 + \frac{55R}{55 + R} = 35
\]

### Step 3: Solve for \( R \)
Simplify and solve the equation:
\[
\frac{55R}{55 + R} = 35 - 12
\]
\[
\frac{55R}{55 + R} = 23
\]
Now multiply both sides by \( 55 + R \):
\[
55R = 23(55 + R)
\]
\[
55R = 23 \times 55 + 23R
\]
\[
55R = 1265 + 23R
\]
Subtract \( 23R \) from both sides:
\[
32R = 1265
\]
Solve for \( R \):
\[
R = \frac{1265}{32} = 39.53 \, \Omega
\]

So, the value of \( R \) is approximately **39.53 Ω**.

Would you like more details or further explanation? Here are some related questions for deeper understanding:

1. How do you calculate the total resistance in parallel and series circuits?
2. What are some typical applications of resistors in electrical circuits?
3. How does the value of a parallel resistor affect the total resistance in the circuit?
4. How can Kirchhoff's laws be used to solve complex circuits?
5. What happens to the circuit if the value of \( R \) changes significantly?

**Tip:** Always double-check the configuration of resistors (whether series or parallel) before solving, as it can drastically change the results.

The equivalent resistance between points A and B of the resistors shown in the figure is 35 Ω. Find the value of resistance R.

Learn how to calculate the unknown resistance R in a circuit with resistors in both series and parallel combinations. This problem involves applying algebra and circuit theory to solve for the total equivalent resistance, given specific resistor values. Suitable for students in Grades 10-12.

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